Subject: Chemistry — Chemical Thermodynamics
Question: Consider the following volume-temperature (V-T) diagram
for the expansion of 5 moles of an ideal monoatomic gas.
[IMAGE] Considering on P-V work is involved, the total change in enthalpy (in
Joule) for the transformation of state in the sequence
$X \rightarrow Y \rightarrow Z$ is \_\_\_\_\_\_\_\_.
\[Use the given data: Molar heat capacity of the gas for the given
temperature range, $C_{v},m = 12\ JK^{- 1}mol^{- 1}$ and gas constant,
$R = 8.3\ JK^{- 1}mol^{- 1}$\]
Answer: (8120)
Solution: $X \rightarrow Y$ is an isothermal process and for ideal
bas
$$\mathrm{\Delta}H = 0$$
$Y \rightarrow Z$ is an isochoric process
$$\mathrm{\Delta}U = nC_{V,m}\left( T_{2} - T_{1} \right)$$
$$= 5 \times 12(415 - 335)$$
$$= 4800\ J$$
$$\mathrm{\Delta}H = \mathrm{\Delta}U + \mathrm{\Delta}(PV)$$
$$= \mathrm{\Delta}U + nR\mathrm{\Delta}T$$
$$= 4800 + 5 \times 8.3 \times (415 - 335)$$
$$= 8120\ J$$